Let F_1 & F_2 be the foci of an ellipse f | vedclass

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Question

angle bisectors are either tangents or normals to

the ellipse $\mathrm{y}=\mathrm{mx} \pm \sqrt{\mathrm{a}^{2} \mathrm{m}^{2}+\mathrm{b}^{2}}$

o

Vedclass · Accepted Answer

$y = x + \frac{5}{{\sqrt {13} }}$

Vedclass · Answer

angle bisectors are either tangents or normals to

the ellipse $\mathrm{y}=\mathrm{mx} \pm \sqrt{\mathrm{a}^{2} \mathrm{m}^{2}+\mathrm{b}^{2}}$

or $\mathrm{y}=\mathrm{mx} \pm \frac{\left(\mathrm{a}^{2}-\mathrm{b}^{2}\right) \mathrm{m}}{\sqrt{\mathrm{a}^{2}+\mathrm{m}^{2} \mathrm{b}^{2}}}$

Now put $\mathrm{m}=1$

$y=x \pm \frac{5}{\sqrt{13}}$

Let $F_1$ & $F_2$ be the foci of an ellipse $\frac{{{x^2}}}{4} + \frac{{{y^2}}}{9} = 1$ such that a ray from $F_1$ strikes the elliptical mirror at the point $P$ and get reflected. Then equation of angle bisector of the angle between incident ray and reflected ray can be

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